Multi-blade fan

ABSTRACT

A multi-blade fan includes a support body rotatable about a rotary shaft, and a plurality of blades secured to the support body such that an inter-blade pitch angle relative to the rotary shaft assumes a prescribed arrangement. The blades extend along an axial direction of the rotary shaft. The plurality of blades are disposed such that, with respect to amplitude values of periodic functions at individual orders when the prescribed arrangement is expanded in a periodic Fourier series, a maximum amplitude value is less than 200% of a second-largest amplitude value.

CROSS-REFERENCE TO RELATED APPLICATIONS

This U.S. National stage application claims priority under 35 U.S.C. §119(a) to Japanese Patent Application No. 2013-272150, filed in Japan onDec. 27, 2013, the entire contents of which are hereby incorporatedherein by reference.

TECHNICAL FIELD

The present invention relates to a cross-flow fan or other type ofmulti-blade fan.

BACKGROUND ART

There are conventionally known blowers in which a cross-flow fan orother type of multi-blade fan is used, wherein wind noise is produced bymultiple blades. To counteract a wind noise component having afundamental frequency related to the number of rotations N and thenumber of blades Z (referred to below as “NZ noise”) from within thewind noise, values of the angle of the pitch between the blades of thecross-flow fan are arranged at random (random pitch angle arrangement),whereby the inter-blade pitch angle arrangement is varied to reducenoise. Such variation of the inter-blade pitch angle arrangementproduces increases/decreases and/or time distortion in acoustic-pressurefluctuation, which causes the NZ noise, to offset the timing at whichthe NZ noise is generated, making it possible to minimize increases inunpleasant noise by reducing the prominence of NZ noise having acharacteristic frequency.

However, in conventional methods for determining such inter-blade pitchangle arrangements randomly, the amount by which the NZ noise is reducedchanges for each determination of the arrangement, resulting in anunpredictable, ad-hoc method of solution.

Furthermore, there are many cases in which the randomly determinedarrangement coincidentally matches an inter-blade pitch anglearrangement in which noise is prominent at low frequencies; in order toobtain an optimal arrangement in which noise prominent at lowfrequencies is suppressed while significantly reducing NZ noise, it isnecessary repeatedly to perform a process of trial-and-error. This isnot an efficient method for determining the inter-blade pitch anglearrangement for blowers in which the cross-flow fans have differentspecifications, such as with respect to number of blades.

In the method for determining inter-blade pitch angle arrangementdescribed in, e.g., Japanese Patent No. 3484854, an arrangement isimparted such that a sine waveform of a particular order is obtainedwhen the inter-blade pitch angle arrangement is expanded in a Fourierseries. When the inter-blade pitch angle arrangement is determined inthis manner, the NZ noise is linked to the reduction of low-frequencybroadband noise.

SUMMARY Technical Problem

However, although NZ noise and low-frequency broadband noise are reducedin the determination method of Japanese Patent No. 3484854, the rotationnoise of the cross-flow fan having the order used in the sine wave;i.e., discrete-frequency noise relating to a rotation speed (referred tobelow as “N noise”) alone is increasingly independently prominent. Thislow-frequency, independently prominent noise is an unpleasant abnormalnoise similar to the NZ noise, inhibiting a noise-reduction propertyintended to improve the multi-blade fan.

The problem of the present invention is to provide a multi-blade fan inwhich the prominence of wind noise, low-frequency broadband noise, andspecific discrete-frequency noise is minimized, and in which anoise-reduction property is enhanced.

Solution to Problem

A multi-blade fan according to a first aspect of the present inventioncomprises: a support body that rotates about a rotary shaft; and aplurality of blades secured to the support body such that an inter-bladepitch angle relative to the rotary shaft assumes a prescribedarrangement, the blades extending along an axial direction of the rotaryshaft; the plurality of blades being disposed such that, with respect tothe amplitude values of periodic functions at individual orders when theprescribed arrangement is expanded in a periodic Fourier series, themaximum amplitude value is less than 200% of the second-largestamplitude value.

In the multi-blade fan according to the first aspect, because themaximum amplitude value is less than 200% of the second-largestamplitude value with respect to the amplitude values of periodicfunctions at individual orders when the prescribed disposition isexpanded in a periodic Fourier series, the inhibiting of noisereduction, caused by the prominence of only a order having the maximumamplitude and the production of unpleasant low-frequency noise, ismitigated.

A multi-blade fan according to a second aspect of the present inventionis the multi-blade fan according to the first aspect of the presentinvention, wherein the plurality of blades are disposed such that, withrespect to the amplitude values of periodic functions at individualorders of the periodic Fourier series, the second-largest amplitudevalue and the third-largest amplitude value are within a range of50-100% of the maximum amplitude value.

In the multi-blade fan according to the second aspect, because theperiodic function having the second-largest amplitude value and theperiodic function having the third-largest amplitude value have anamplitude value that is within a range of 50-100% of the maximumamplitude value, the magnitudes of the amplitude values of periodicfunctions having large relative amplitude values are not far removedfrom each other; therefore, the effects of not only the periodicfunction having the maximum amplitude value but also the periodicfunction having the second-largest amplitude value are insignificant.

A multi-blade fan according to a third aspect of the present inventionis the multi-blade fan according to the second aspect of the presentinvention, wherein the plurality of blades are disposed such that theamplitude values of periodic functions at a number of orders equal to orgreater than one-third of the total number of orders of the periodicFourier series are within a range of 50-100% of the maximum amplitudevalue.

In the multi-blade fan according to the third aspect, because the numberof orders having large relative amplitude values, such that themagnitude of the amplitude values of the periodic functions are within arange of 50-100% of the maximum amplitude value, accounts for one-thirdor more of the total number of orders, the effects of not only theperiodic function having the maximum amplitude value but also otherperiodic functions having large amplitude values are insignificant.

A multi-blade fan according to a fourth aspect of the present inventionis the multi-blade fan according to the third aspect of the presentinvention, wherein the plurality of blades are disposed such that theamplitude values of periodic functions at a number of orders equal to orgreater than one-half of the total number of orders of the periodicFourier series are within a range of 50-100% of the maximum amplitudevalue.

In the multi-blade fan according to the fourth aspect, because thenumber of orders having large relative amplitude values, such that themagnitude of the amplitude values of the periodic functions are within arange of 50-100% of the maximum amplitude value, accounts for one-halfor more of the total number of orders, the effects of not only theperiodic function having the maximum amplitude value but also otherperiodic functions having large amplitude values are insignificant.

A multi-blade fan according to a fifth aspect of the present inventionis the multi-blade fan according to any of the first through fourthaspects of the present invention, wherein the plurality of blades aresuch that a selection is made from lower orders where the order of aperiodic function that has an amplitude value within a range of 50-100%of the maximum amplitude value is two or greater.

In the multi-blade fan according to the fifth aspect, because theamplitude values of low-order-side periodic functions are grouped so asto be within a range of 50-100% of the maximum amplitude value, theeffect for dispersing NZ noise is enhanced.

A multi-blade fan according to a sixth aspect of the present inventionis the multi-blade fan according to any of the first through fifthaspects of the present invention, wherein the plurality of blades aredisposed such that a first-order amplitude value when the prescribedarrangement is expanded in a periodic Fourier series is zero.

In the multi-blade fan according to the sixth aspect, because theamplitude value of a first-order periodic function is zero, the centerof gravity does not significantly deviate from the shaft.

Advantageous Effects of Invention

In the multi-blade fan according to the first aspect of the presentinvention, it is possible not only to reduce wind noise andlow-frequency broadband noise, but also to suppress the prominence ofspecific discrete-frequency noise and to enhance a noise-reductionproperty.

In the multi-blade fan according to the second aspect of the presentinvention, the unpleasantness of noise generated along with the rotationof the multi-blade fan is mitigated.

In the multi-blade fan according to the third aspect of the presentinvention, the effect for mitigating the unpleasantness of noisegenerated along with the rotation of the multi-blade fan is enhanced.

In the multi-blade fan according to the fourth aspect of the presentinvention, the effect for mitigating the unpleasantness of noisegenerated along with the rotation of the multi-blade fan is enhanced.

In the multi-blade fan according to the fifth aspect of the presentinvention, a multi-blade fan having a high NZ-noise-dispersing effect isobtained.

In the multi-blade fan according to the sixth aspect of the presentinvention, it is possible to minimize problems due to disruption torotational balance.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic cross-sectional view of an indoor unit in anair-conditioning apparatus;

FIG. 2 is a schematic perspective view of an impeller of a cross-flowfan according to a first embodiment;

FIG. 3 is a top view for illustrating the disposition of a plurality ofblades of the cross-flow fan;

FIG. 4 is a graph showing one example of a relationship between sinefunction order and amplitude value according to an embodiment;

FIG. 5 is a graph for illustrating inter-blade pitch angle arrangements;

FIG. 6 is a graph showing one example of a conventional relationshipbetween sine function order and amplitude value;

FIG. 7 is a graph showing one example of a conventional relationshipbetween sine function order and amplitude value;

FIG. 8 is a graph showing noise values for each rotation-order frequencygenerated by a cross-flow fan having the characteristics illustrated inFIG. 4;

FIG. 9 is a graph showing noise values for each rotation-order frequencygenerated by a cross-flow fan having the characteristics illustrated inFIG. 6; and

FIG. 10 is a graph showing noise values for each rotation-orderfrequency generated by a cross-flow fan having the characteristicsillustrated in FIG. 7.

DESCRIPTION OF EMBODIMENTS

(1) Cross-Flow Fan Inside Indoor Unit

A cross-flow fan according to a first embodiment of the presentinvention is described below through the example of a cross-flow faninstalled in an indoor unit of an air-conditioning apparatus. FIG. 1 isa schematic view of a cross-section of an indoor unit 1 of anair-conditioning apparatus. The indoor unit 1 comprises a main casing 2,an air filter 3, an indoor heat exchanger 4, a cross-flow fan 10, avertical flap 5, and a horizontal flap 6.

As shown in FIG. 1, the air filter 3 is disposed downstream from anintake port 2 a in a ceiling surface of the main casing 2 so as to facethe intake port 2 a. The indoor heat exchanger 4 is disposed furtherdownstream from the air filter 3. The indoor heat exchanger 4 isconfigured by coupling a front-surface-side heat exchanger 4 a and arear-surface-side heat exchanger 4 b so as to form an inverse V-shape asviewed from a side surface. The front-surface-side heat exchanger 4 aand the rear-surface-side heat exchanger 4 b are configured by attachinga plurality of plate fins to a heat-transfer pipe aligned in parallelwith a width direction of the indoor unit 1. All of indoor air thatpasses through the intake port 2 a and reaches the indoor heat exchanger4 passes through the air filter 3, and dirt and grit in the indoor airis removed therefrom. The indoor air that has been drawn in through theintake port 2 a and passed through the air filter 3 is subjected toheat-exchange and air-conditioning when passing between the plate finsof the front-surface-side heat exchanger 4 a and rear-surface-side heatexchanger 4 b.

The cross-flow fan 10, which is substantially cylindrical in shape, isprovided downstream from the indoor heat exchanger 4 so as to extendlongitudinally along a width direction of the main casing 2. Thecross-flow fan 10 is disposed in parallel with the indoor heat exchanger4. The cross-flow fan 10 comprises an impeller 20 disposed in a spacesurrounded so as to be sandwiched in the inverse V-shape of the indoorheat exchanger 4, and a fan motor (not shown) configured and arranged todrive the impeller 20. The cross-flow fan 10 generates an airflow fromthe indoor heat exchanger 4 toward a vent 2 b by the rotation of theimpeller 20 in a direction A1 shown by arrows in FIG. 1 (i.e.,clockwise). Specifically, the cross-flow fan 10 is a transverse fan,configured such that the airflow passes transversely across thecross-flow fan 10.

A rear-surface side of a vent passage linked to the vent 2 b downstreamfrom the cross-flow fan 10 is configured from a scroll member 2 c. Alower end of the scroll member 2 c is coupled to a lower edge of anopening of the vent 2 b. In order to guide indoor air, which is ventedout from the cross-flow fan 10, smoothly and silently to the vent 2 b, aguide surface of the scroll member 2 c has a smooth curved shape havinga center of curvature on the cross-flow-fan 10 side as viewed incross-section. A tongue part 2 d is formed on the front-surface side ofthe cross-flow fan 10, and an upper surface of the vent passage that iscontinuous from the tongue part 2 d is coupled to an upper edge of thevent 2 b. A direction in which the airflow is vented out from the vent 2b is adjusted using the vertical flap 5 and horizontal flap 6.

(2) Blade Structure of Cross-Flow Fan

FIG. 2 shows a schematic structure of the impeller 20 of the cross-flowfan 10. The impeller 20 is configured such that, e.g., end plates 21, 24and a plurality of fan blocks 30 are joined together. In the presentexample, seven fan blocks 30 are joined together. An end plate 21 isdisposed on one end of the impeller 20, and a metal rotary shaft 22 isprovided along a central axis O. Each of the fan blocks 30 comprises aplurality of blades 100 and an annular support plate 50.

FIG. 3 shows the disposition of a plurality of blades 100 secured to thesupport plate 50 of one of the fan blocks 30. The plurality of blades100 shown in FIG. 3 comprise 35 blades, from a first blade 101 to a35^(th) blade 135. In FIG. 3, chain lines extending radially from acenter of the support plate 50 indicate reference lines BL configuredand arranged to determine inter-blade pitch angles Pt1-Pt35. In a topview, the reference lines BL are tangent lines that pass through thecenter of the support plate 50 and contact the blade-outer-peripheralsides of each of the first through 35^(th) blades 101-135. The angleformed by the reference line BL of the first blade 101 and the referenceline BL of the second blade 102 is a first inter-blade pitch angle Pt1,the angle formed by the reference line BL of the second blade 102 andthe reference line BL of the third blade 103 is a second inter-bladepitch angle Pt2, etc.; the angle formed by the reference line BL of the35^(th) blade 135 and the reference line BL of the first blade 101 is a35^(th) inter-blade pitch angle Pt35. In descriptions given below, thesymbol numbers from the first inter-blade pitch angle Pt1 to the 35^(th)inter-blade pitch angle Pt35 are referred to as “pitch numbers.”Specifically, the pitch number of the first inter-blade pitch angle Pt1is 1, the pitch number of the second inter-blade pitch angle Pt2 is 2,etc., and the pitch number of the 35^(th) inter-blade pitch angle Pt35is 35.

In the fan block of the cross-flow fan 10 in FIG. 3, the value θ_(k) ofthe k^(th) inter-blade pitch angle Ptk of pitch number k (where k=1, . .. , 35) is disposed in an inter-blade pitch angle arrangement θ_(k)given by formula (1), the inter-blade pitch angle arrangement θ_(k)being expanded in a periodic Fourier series. In formula (1), Z indicatesthe number of blades 100 disposed around the circumference, and A1indicates the maximum order value. The maximum value of the order of thesine functions is given by the largest integer that does not exceed thevalue obtained by dividing the number of blades by 2.

$\begin{matrix}{< {{Formula}\mspace{14mu} 1} >} & \; \\{{\theta_{k} = {\theta_{0} + {\sum\limits_{m = 1}^{M}\;{\alpha_{m} \cdot {\sin\left( {{2\pi\frac{mk}{Z}} + \beta_{m}} \right)}}}}}{\left( {{k = 1},\Lambda,Z} \right),\begin{pmatrix}{M = {\frac{Z}{2}\left( {{where}\mspace{14mu} Z\mspace{14mu}{is}\mspace{14mu}{even}} \right)}} \\{{M = \frac{\left( {Z - 1} \right)}{2}\left( {{where}\mspace{14mu} Z\mspace{14mu}{is}\mspace{14mu}{odd}} \right)}\mspace{11mu}}\end{pmatrix}}} & (1)\end{matrix}$

In the formula, Z is a natural number equal to or greater than 6;

k=1, Λ, Z (where k is a natural number);

m=1, Λ, M (where m is a natural number);

θ_(k)=arrangement of each of the inter-blade pitch angles (degree);

$\theta_{0} = \frac{360}{Z}$(angle in the case of equal-interval pitches) (degree);

α_(m)=amplitude value of sine functions of order m; and

β_(m)=phase shift of sine functions of order m.

The inter-blade pitch angle arrangement θ_(k) is determined inaccordance with the following stipulations.

In formula (1), with respect to an amplitude value α_(m) of the sinefunctions of individual orders m, when the maximum amplitude value isdesignated as αmax and the second-largest amplitude value is designatedas α2nd, the amplitude values are determined so as to satisfy therelationship αmax<2×α2nd. Specifically, the inter-blade pitch anglearrangement θ_(k) is an arrangement in which the maximum amplitude valueαmax is less than 200% of the second-largest amplitude value α2nd. Suchan inter-blade pitch angle arrangement θ_(k) is referred to below as a“low-N-noise arrangement.”

FIG. 4 is a graph showing one example of the relationship between sinefunction order and amplitude value, for forming a low-N-noisearrangement. Because there are 35 blades in the plurality of blades 100,it is possible to represent the inter-blade pitch angle arrangementθ_(k) by using the sum from the first-order sine function through the17^(th)-order sine function when the inter-blade pitch angle arrangementθ_(k) is expanded in a periodic Fourier series using sine functions.

As shown in FIG. 4, the amplitude value α₁ of the first-order sinefunction is 0. The amplitude values α₂, α₃, α₄, as from the second-ordersine function through the fifth-order sine function are all 250. Theamplitude values α₉, α₁₀, α₁₁, α₁₂, α₁₃, α₁₄, α₁₅, α₁₆, α₁₇ from theninth-order sine function through the 17^(th)-order sine function areall 200. The amplitude values α₆, α₇, α₈ from the sixth-order sinefunction through the eighth-order sine function are between 250 and 200,becoming smaller in sequence. Comparing the amplitude values α₁-α₁₇ ofthese sine functions reveals that the maximum amplitude value αmax andthe second-largest amplitude value α2nd are included in the amplitudevalues α₂, α₃, α₄, as from the second-order sine function through thefifth-order sine function. Specifically, in the low-N-noise arrangementhaving the characteristics illustrated in FIG. 4, the conditionsαmax=α2nd and αmax<2×α2nd are satisfied.

The low-N-noise arrangement having the characteristics illustrated inFIG. 4 is furthermore disposed such that the second-largest amplitudevalue α2nd and the third-largest amplitude value α3rd are within a rangeof 50-100% of the maximum amplitude value with respect to the amplitudevalues α_(m) of the sine functions at individual orders m. Specifically,the maximum amplitude value αmax, the second-largest amplitude valueα2nd, and the third-largest amplitude value α3rd satisfy therelationships αmax/2≤α2nd≤αmax, and αmax/2≤α3rd≤αmax. With reference toFIG. 4, because the amplitude values α₂, α₃, α₄, α₅ from thesecond-order sine function through the fifth-order sine function are all250, the relationship αmax=α2nd=α3rd=α4th is satisfied. α4th is thefourth-largest amplitude value.

In the low-N-noise arrangement having the characteristics illustrated inFIG. 4, the amplitude values of 15 orders other than the first order areequal to or greater than 125, which is half of the maximum amplitudevalue αmax; 15 of the 17 orders are within a range of 75-100% of themaximum amplitude value αmax. Specifically, in the low-N-noisearrangement having the characteristics illustrated in FIG. 4, theamplitude values α_(m) (m=2, . . . , 17) of the sine functions at ordersnumbering one-third of the total number of orders of the periodicFourier series, and furthermore at orders numbering one-half of thetotal number of orders of the periodic Fourier series, are within arange of 50-100% of the maximum amplitude value αmax.

Moreover, a selection is made from lower orders where the order of asine function that has an amplitude value within a range of 50-100% ofthe maximum amplitude value αmax is two or greater. Although difficultto understand from the low-N-noise arrangement having thecharacteristics illustrated in FIG. 4, this means that sine functionsfrom the second order to the fifth order are sequentially selected fromthe lower orders of two and greater in the following sequence: sinefunction having the maximum amplitude value αmax, sine function havingthe second-largest amplitude value α2nd, sine function having thethird-largest amplitude value α3rd, and sine function having thefourth-largest amplitude value α4th. For example, the amplitude valueα_(m) should be determined so that an amplitude value α_(n) having acertain order and belonging to amplitude values α_(m) (m=2, . . . , 17)having an order except one is equal to or greater than an amplitudevalue α_(n+1) having a higher order than the order of the amplitudevalue α_(n).

Because this concept is difficult to understand from the low-N-noisearrangement having the characteristics illustrated in FIG. 4, an exampleis given in which the amplitude value α4 of a fourth-order sine functionis αmax=300, where α2nd=290, α3rd=280, and smaller amplitude values arerespectively equal to 270, 260, 250, 240, 230, 220, 210, 100, 90, 80,70, 60, 50, and 0. In this case, the order of the sine functions isselected such that, e.g., the amplitude value α₂ of a second-order sinefunction is 290, the amplitude value α₃ of a third-order sine functionis 280, the amplitude value α₅ of a fifth-order sine function is 270,the amplitude value α₆ of a sixth-order sine function is 260, theamplitude value α₇ of a seventh-order sine function is 250, theamplitude value α₈ of an eighth-order sine function is 240, theamplitude value α₉ of a ninth-order sine function is 230, the amplitudevalue α₁₀ of a tenth-order sine function is 220, and the amplitude valueα₁₁ of an eleventh-order sine function is 210. In this case, the sinefunctions of orders higher than twelve may be selected in any manner.However, as shall be described later, the amplitude value α1 of afirst-order sine function is preferably selected so as to be the minimumamplitude value αmin; i.e., zero. In this case as well, the inter-bladepitch angle arrangement θ_(k) is configured such that the amplitudevalues α_(m) (m=2, 3, 5, . . . , 11) of the sine functions at ordersnumbering one-half of the total number of orders of the periodic Fourierseries are disposed within a range of 50-100% of the maximum amplitudevalue αmax.

With respect to the amplitude values α_(m), it is furthermore preferableto set the amplitude values of all of the orders included in m>M/2 so asto be 0.6-0.8 times the amplitude value α2 of the second-order sinefunction. Setting the amplitude values in this manner enhances theeffect for dispersing NZ noise.

In the low-N-noise arrangement having the characteristics illustrated inFIG. 4, the amplitude value α1 of the first-order sine function is 0. Ina case in which a configuration is adopted as described above, and anarrangement is adopted such that N noise can be minimized, only theamplitude value α1 of the first-order sine function contributes torotational balance; therefore, a design can be adopted such that, whenthe amplitude value α₁ of the first-order sine function approaches zero,the center of gravity in a cross-section perpendicular to the rotationalaxis O of the cross-flow fan 10 does not substantially deviate from theaxis. For this reason, the amplitude value α₁ of the first-order sinefunction is set to 0 in the low-N-noise arrangement having thecharacteristics illustrated in FIG. 4.

FIG. 5 shows three inter-blade pitch angle arrangement θ_(k). In FIG. 5,the inter-blade pitch angle arrangement θ_(k) indicated by graph G1,which is plotted using triangles, is a low-N-noise arrangement havingthe characteristics illustrated in FIG. 4. The amplitude value α_(m) ofthe sine functions is preferably set as described above in order tominimize N noise, and the effect for minimizing N noise can be obtainedirrespective of the method in which the phase shift β_(m) is set;therefore, the low-N-noise arrangement shown in FIG. 5 is obtained bysuitably setting the phase shift β_(m) such that the difference betweenthe maximum value and minimum value of the inter-blade pitch anglearrangement θ_(k) is not particularly large. For example, when aninter-blade pitch angle θ₂ of pitch number 2 is applied to an actual fanblock 30, the interval between the blade 101 and the blade 102 isdetermined such that the inter-blade pitch angle Pt2 in FIG. 3 is θ2.

(3) Characteristics

(3-1)

As described above, the plurality of blades 100, 101-135 of thecross-flow fan (an example of a multi-blade fan) are secured to thesupport plate 50 (an example of a support body). The plurality of blades100, 101-135 are disposed in a low-N-noise arrangement (an example of aprescribed arrangement) having the characteristics illustrated in FIG. 4such that, with respect to the amplitude values α_(m) of the sinefunctions (an example of periodic functions) at individual orders whenthe inter-blade pitch angle arrangement θ_(k) is expanded in a periodicFourier series, the maximum amplitude value αmax is 250, the same as thesecond-largest amplitude value α2nd. Specifically, it is possible toconsider a disposition such that the maximum amplitude value αmax isless than 200% of the second-largest amplitude value α2nd. As a result,the inhibition of noise reduction, caused by the prominence of only aorder that has the maximum amplitude value αmax and the production ofunpleasant low-frequency noise, is mitigated. Specifically, a cross-flowfan 10 configured using a fan block 30 shown in FIG. 3 that has aninter-blade pitch angle arrangement θ_(k) such as is shown in the graphG1 of FIG. 5 makes it possible not only to reduce wind noise andlow-frequency broadband noise, but also to suppress the prominence ofspecific discrete-frequency noise and to enhance a noise-reductionproperty.

In particular, in the low-N-noise arrangement having the characteristicsillustrated in FIG. 4, the plurality of blades 100, 101-135 are disposedsuch that, with respect to the amplitude values α_(m) of the sinefunctions at individual orders when the inter-blade pitch anglearrangement θ_(k) is expanded in a periodic Fourier series, thesecond-largest amplitude value α2nd and the third-largest amplitudevalue α3rd are 250, the same as the maximum amplitude value αmax.Specifically, it is possible to consider a disposition such that thesecond-largest amplitude value α2nd and the third-largest amplitudevalue α3rd are within a range of 50-100% of the maximum amplitude valueαmax. As a result, the magnitudes of the amplitude values of sinefunctions having large relative amplitude values are not far removedfrom each other; therefore, the effects of not only the sine functionhaving the maximum amplitude value αmax but also the sine functionhaving the second-largest amplitude value are insignificant.

This effect increases in accordance with increases in the orders withina range of 50-100% of the maximum amplitude value αmax; a dispositionsuch that the amplitude values of the sine functions at a number oforders equal to or greater than one-third of the total number of ordersof the periodic Fourier series are within a range of 50-100% of themaximum amplitude value is preferred, and a disposition such that theamplitude values of the sine functions at a number of orders equal to orgreater than one-half of the total number of orders of the periodicFourier series are within a range of 50-100% of the maximum amplitudevalue is more highly preferred.

This effect will be described in detail while comparing a cross-flow fanhaving a random pitch angle arrangement in which the blades are disposedat uneven intervals having randomly varied pitch angles, and thecross-flow fan disclosed in Patent Document 1. In the cross-flow fandisclosed in Patent Document 1, only the amplitude value α₂ of thesecond-order sine function has a value when the inter-blade pitch anglearrangement is expanded in a periodic Fourier series; the amplitudevalues of the sine functions of other orders are zero. In cases in whichthis configuration is applied to a cross-flow fan having 35 blades,similarly to the embodiment of the present invention, the blades aredisposed so as to have an inter-blade pitch angle arrangement θ_(k)expanded in a periodic Fourier series such as is shown in FIG. 6. Theinter-blade pitch angle arrangement θ_(k) expanded in a periodic Fourierseries shown in FIG. 6 is the inter-blade pitch angle arrangement θ_(k)indicated by graph G2, which is plotted using squares, in FIG. 5. Oneexample of a cross-flow fan having a random pitch angle arrangement hasthe inter-blade pitch angle arrangement θ_(k) expanded in a periodicFourier series shown in the graph in FIG. 7. The inter-blade pitch anglearrangement θ_(k) expanded in the periodic Fourier series shown in thegraph in FIG. 7 is the inter-blade pitch angle arrangement θ_(k)indicated by graph G3, which is plotted using rhombuses, in FIG. 5.

FIG. 8 is a graph obtained by performing a Fourier transform on thenoise generated by the cross-flow fan 10, and indicating noise valuesfor each rotation-order frequency. FIG. 9 is a graph obtained byperforming a Fourier transform on the noise generated by a cross-flowfan having the inter-blade pitch angle arrangement θ_(k) illustrated inFIG. 6, and indicating noise values for each rotation-order frequency.FIG. 10 is a graph obtained by performing a Fourier transform on thenoise generated by a cross-flow fan having the inter-blade pitch anglearrangement θ_(k) illustrated in FIG. 7, and indicating noise values foreach rotation-order frequency. The second-order rotation-order frequencyis, e.g., 2×the number of rotations (rpm/60). The same scale is used onthe vertical axes of FIGS. 8, 9, and 10 for ease of comparison. Althoughthe numerical values on this scale have no significance in and ofthemselves, they express the logarithm of the ratio relative to areference amount in order to allow the noise values to be compared.

It can be expected that low-frequency noise having the same frequency asthe second-order sine function will be prominent in a cross-flow fanhaving an inter-blade pitch angle arrangement θ_(k) such as is shown inFIG. 6, as shall be apparent. Actually, as shown in FIG. 9, second-orderrotation-order N noise is strongly prominent; such noise is perceived asunnatural and unusually unpleasant because sound corresponding to astrongly prominent rotation order is present in a low-frequency band.Thus, in a cross-flow fan having an inter-blade pitch angle arrangementθ_(k) obtained by expanding a Fourier series configured only fromsecond-order sine functions, the energy of NZ noise is disperseddisproportionately only at certain rotation-order frequencies, and therotation-order frequencies at which the dispersed energy is dispersedare limited. Noise in which frequencies other than the NZ frequenciesare prominent is therefore generated.

It is apparent from FIG. 10 that the amplitude value of a frequencycorresponding to a 16^(th)-order sine function is prominent. In across-flow fan having an inter-blade pitch angle arrangement θ_(k) suchas is illustrated by graph G3 in FIG. 5, the energy of NZ noise (noisecorresponding to a 35^(th)-order rotation-order frequency) is dispersedat other rotation-order frequencies; however, because the inter-bladepitch angle arrangement θ_(k) is determined randomly, audibly unpleasantnoise is generated as a result, due to the prominence of the amplitudevalue at a frequency corresponding to the 16^(th)-order sine function.

As seen in the distribution of noise values at the rotation-orderfrequencies shown in FIG. 8, it is apparent that these NZ noise valuesare lower than those shown in FIGS. 9 and 10, and that the energy ismore widely dispersed at other rotation-order frequencies than in FIGS.9 and 10 in correspondence with this reduction in NZ noise. Therefore,irrespective of the great reduction in NZ noise, the generation of Nnoise is also minimized. As a result, in the cross-flow fan 10, it ispossible not only to reduce wind noise and low-frequency broadbandnoise, but also to suppress the prominence of specificdiscrete-frequency noise and to enhance a noise-reduction property.

(3-2)

Additionally, in the plurality of blades 100, 101-135, a selection ismade from lower orders where the order of a sine function that has anamplitude value within a range of 50-100% of the maximum amplitude valueis two or greater. Because the amplitude values of low-order-sideperiodic functions are grouped so as to be within a range of 50-100% ofthe maximum amplitude value, the effect for dispersing NZ noise in thecross-flow fan 10 is enhanced. For example, as in the low-N-noisearrangement having the characteristics illustrated in FIG. 4, theamplitudes of second-order to eighth-order sine functions are close tothe maximum amplitude value αmax, and the amplitude values of thesecond-order to fifth-order sine functions are uniformly increased so asto approach the maximum amplitude value αmax, whereby a highNZ-noise-dispersing effect is obtained. Additionally, the amplitudes ofsecond-order to eighth-order sine functions are set to 0.8 or more ofthe maximum amplitude value αmax, whereby a further improvedNZ-noise-dispersing effect is obtained.

(3-3)

The plurality of blades 100, 101-135 are disposed in a low-N-noisearrangement having the characteristics illustrated in FIG. 4, such thatthe first-order amplitude value when the inter-blade pitch anglearrangement is expanded in a periodic Fourier series is zero, and aredisposed such that the center of gravity does not significantly deviatefrom the shaft. Having the blades be disposed in this manner reduces thelikelihood of disruption to the rotational balance of the cross-flow fan10, and makes it possible to minimize problems due to any suchdisruption.

(4) Modifications

(4-1)

In the embodiment given above, a description is given using a cross-flowfan as an example of a multi-blade fan. However, the multi-blade fans towhich the present invention can be applied are not limited to transversefans such as cross-flow fans; rather, the present invention can beapplied to centrifugal fans or other multi-blade fans.

(4-2)

In the embodiment given above, sine functions are used as the periodicfunctions when the prescribed disposition is to be expanded in aperiodic Fourier series. However, periodic functions other than sinefunctions; e.g., cosine functions or the like, may be used.

What is claimed is:
 1. A multi-blade fan comprising: a support bodyrotatable about a rotary shaft; and a plurality of blades secured to thesupport body such that an inter-blade pitch angle relative to the rotaryshaft assumes a prescribed arrangement, the blades extending along anaxial direction of the rotary shaft, the plurality of blades beingdisposed such that, with respect to amplitude values of periodicfunctions at individual orders when the prescribed arrangement isexpanded in a periodic Fourier series, a maximum amplitude value is lessthan 200% of a second-largest amplitude value, the amplitude valuesbeing determined such that a first amplitude value having a certainorder and belonging to amplitude values having an order except one isequal to or greater than a second amplitude value having a higher orderthan the order of the first amplitude value, the second amplitude valueis equal to or greater than a third amplitude value having a higherorder than the order of the second amplitude value, the third amplitudevalue is equal to or greater than a fourth amplitude value having ahigher order than the order of the third amplitude value, and the fourthamplitude value is equal to or greater than a fifth amplitude valuehaving a higher order than the order of the fourth amplitude value, witheach (n+1)-order amplitude value being equal to or greater than each(n+2)-order amplitude value, wherein n represents an integer of 1through
 15. 2. The multi-blade fan according to claim 1, wherein theplurality of blades are disposed such that, with respect to theamplitude values of periodic functions at individual orders of theperiodic Fourier series, the second-largest amplitude value is equal toor less than 100% of the maximum amplitude value and the third-largestamplitude value is within a range of 50-100% of the maximum amplitudevalue.
 3. A multi-blade fan comprising: a support body rotatable about arotary shaft; and a plurality of blades secured to the support body suchthat an inter-blade pitch angle relative to the rotary shaft assumes aprescribed arrangement, the blades extending along an axial direction ofthe rotary shaft, the plurality of blades being disposed such that, withrespect to amplitude values of periodic functions at individual orderswhen the prescribed arrangement is expanded in a periodic Fourierseries, a maximum amplitude value is less than 200% of a second-largestamplitude value, the plurality of blades being disposed such that theamplitude values of periodic functions at a number of orders equal to orgreater than one-half of a total number of orders of the periodicFourier series are within a range of 50-100% of the maximum amplitudevalue, the plurality of blades being disposed such that a selection ismade from lower orders where the order of a periodic function that hasan amplitude value within a range of 50-100% of a maximum amplitudevalue is two or greater, and the plurality of blades being disposed suchthat a first-order amplitude value when the prescribed arrangement isexpanded in a periodic Fourier series is less than 50% of the maximumamplitude value.
 4. The multi-blade fan according to claim 3, whereinthe plurality of blades are disposed such that, with respect to theamplitude values of periodic functions at individual orders of theperiodic Fourier series, the second-largest amplitude value is equal toor less than 100% of the maximum amplitude value and the third-largestamplitude value is within a range of 50-100% of the maximum amplitudevalue.
 5. The multi-blade fan according to claim 3, wherein theplurality of blades are disposed such that the first-order amplitudevalue when the prescribed arrangement is expanded in a periodic Fourierseries is zero.
 6. A multi-blade fan comprising: a support bodyrotatable about a rotary shaft; and a plurality of blades secured to thesupport body such that an inter-blade pitch angle relative to the rotaryshaft assumes a prescribed arrangement, the blades extending along anaxial direction of the rotary shaft, the plurality of blades beingdisposed such that, with respect to amplitude values of periodicfunctions at individual orders when the prescribed arrangement isexpanded in a periodic Fourier series, a maximum amplitude value is lessthan 200% of a second-largest amplitude value, the plurality of bladesbeing disposed such that the amplitude values of periodic functions at anumber of orders equal to or greater than one-half of a total number oforders of the periodic Fourier series are within a range of 50-100% ofthe maximum amplitude value, and the plurality of blades being disposedsuch that a first-order amplitude value when the prescribed arrangementis expanded in a periodic Fourier series is zero.
 7. The multi-blade fanaccording to claim 6, wherein the plurality of blades are disposed suchthat, with respect to the amplitude values of periodic functions atindividual orders of the periodic Fourier series, the second-largestamplitude value is equal to or less than 100% of the maximum amplitudevalue and the third-largest amplitude value is within a range of 50-100%of the maximum amplitude value.